Is sin^2(θ)-cos^2(θ)sin^2(θ)=sin^4(θ) ?

The answer to whether sin^2(θ)-cos^2(θ)sin^2(θ)=sin^4(θ) is True

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prove sin^2(θ)-cos^2(θ)sin^2(θ)=sin^4(θ)

prove

sin^{2} (θ) - cos^{2} (θ) sin^{2} (θ) = sin^{4} (θ)

True

Solution steps

sin^{2} (θ) - cos^{2} (θ) sin^{2} (θ) = sin^{4} (θ)

Manipulating left side

sin^{2} (θ) - cos^{2} (θ) sin^{2} (θ)

Rewrite using trig identities

= sin^{4} (θ)

We showed that the two sides could take the same form

\Rightarrow True

(1 + csc (θ)) (1 - csc (θ)) = - cot^{2} (θ)

cot (u) tan (u) - sin^{2} (u) = cos^{2} (u)

\frac{1}{cos ( θ )} = \frac{tan ( θ )}{sin ( θ )}

(tan (y) + cot (y)) sin (y) cos (y) = 1

sin (x) \cdot cot (x) = cos (x)

Is sin^2(θ)-cos^2(θ)sin^2(θ)=sin^4(θ) ?
The answer to whether sin^2(θ)-cos^2(θ)sin^2(θ)=sin^4(θ) is True